Question

solve for x. round to the nearest tenth, if necessary.

(image of a right triangle tyz with right angle at y, ty = 77, angle at z is 68 degrees, hypotenuse tz is x)

answer attempt 1 out of 2
x = blank submit answer

Explanation:

Step1: Identify the trigonometric ratio

In right triangle \( TYZ \), \( \angle Z = 68^\circ \), the side adjacent to \( \angle Z \) is \( YZ \), the side opposite is \( TY = 77 \), and the hypotenuse is \( x \). We use the sine function because \( \sin(\theta)=\frac{\text{opposite}}{\text{hypotenuse}} \). So, \( \sin(68^\circ)=\frac{77}{x} \).

Step2: Solve for \( x \)

Rearrange the formula to solve for \( x \): \( x = \frac{77}{\sin(68^\circ)} \). Calculate \( \sin(68^\circ) \approx 0.9272 \). Then \( x=\frac{77}{0.9272}\approx 83.0 \).

Answer:

\( 83.0 \)